The human brain contains about 50 billion to 200 billion neurons, each of which interfaces with 1,000 to 100,000 other neurons through 100 trillion (10 ^14) to 10 quadrillion (10^16) synaptic junctions.
Each synapse possesses a variable firing threshold which is reduced as the neuron is repeatedly activated.
If we assume that the firing threshold at each synapse can assume 256 distinguishable levels, and if we suppose that there are 20,000 shared synapses per neuron (10,000 per neuron), then the total information storage capacity of the synapses in the cortex would be of the order of 500 to 1,000 terabytes.
(Of course, if the brain's storage of information takes place at a molecular level, then I would be afraid to hazard a guess regarding how many bytes can be stored in the brain.
One estimate has placed it at about 3.6 X 10^19 bytes.